How much compost to add
Extension services give these amounts: the University of Maryland says 1 inch of compost a year can help keep a garden productive; the University of Minnesota says to work 1 to 2 inches into the top 6 to 8 inches for flowers and vegetables; NC State says raised beds need a 1 to 4 inch layer of organic material after each season. Texas A&M adds a limit: do not add more than a 4-inch layer of organic material.
The University of Minnesota also warns that regular, heavy compost applications can build up phosphorus and salts, which can burn seedling roots.
Topping up a raised bed
Raised bed soil settles as it breaks down. Washington State University Extension says to replenish beds every year or two with fill, compost or both to keep their depth. Measure how far the soil has dropped below where you want it, enter that as the depth, and use the inside size of the bed. For a full refill, use the raised bed soil calculator.
What a yard of compost weighs
The University of Minnesota Extension works with 1,000 lb per cubic yard and says real loads run from 800 to 1,500 lb depending on moisture. The City of Austin gives about 1,000 lb at 40% moisture.